A comparative analysis of the frequency spectra of the human eye and a cut diamond in visible light
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2021-12-07 |
| Journal | Scientific and technical journal of information technologies mechanics and optics |
| Authors | S. I. Zienko, В. Л. Жбанова |
| Institutions | Moscow Power Engineering Institute |
| Citations | 2 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”This research provides a comparative analysis of the frequency spectra of the human eye (visibility curve) and a faceted natural diamond (brilliant), modeling both as dynamic optical systems.
- Dynamic System Equivalence: The optical media of both the human eye and the diamond are successfully modeled as dynamic links, allowing for comparative analysis using control theory metrics.
- Ultra-Wideband (UWB) Properties: Both the eye (day vision µ ≈ 0.72) and the diamond (µ ≈ 0.75) exhibit characteristics of Ultra-Wideband signals (0.2 ≤ µ ≤ 2), indicating extremely fast signal processing capabilities in the femtosecond (fs) range.
- Light Amplification Effect: Both systems demonstrate light amplification (k > 1) in the time domain when the spectrum width (∆f) is less than a critical value (∆fcr = 0.47 x 1015 Hz).
- High Gain Similarity: The light amplification factor (k) for diamond (1.41, or 14.1 dB) is very close to that of the human eye (Night Vision k = 1.38, or 13.8 dB), showing only an insignificant difference.
- Rapid Relaxation: The dielectric relaxation time (τε) for both the eye and diamond is extremely short, approximately 0.8 to 1.13 femtoseconds, confirming the high-speed nature of the electronic polarization response.
- Practical Relevance: The findings support the use of diamond as a superior material for artificial crystalline lenses (IOLs) due to its optical performance closely matching the human eye.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| UWB Index (µ) | 0.72 | Dimensionless | Human Eye (Day Vision) |
| UWB Index (µ) | 0.56 | Dimensionless | Human Eye (Night Vision) |
| UWB Index (µ) | 0.75 | Dimensionless | Diamond Luminescence |
| Light Amplification Factor (k) | 1.24 (12.4 dB) | Dimensionless (dB) | Human Eye (Day Vision) |
| Light Amplification Factor (k) | 1.38 (13.8 dB) | Dimensionless (dB) | Human Eye (Night Vision) |
| Light Amplification Factor (k) | 1.41 (14.1 dB) | Dimensionless (dB) | Diamond |
| Critical Spectrum Width (∆fcr) | 0.47 x 1015 | Hz | Threshold for light amplification (k > 1) |
| Pulse Duration (t0.5) | 1.2 to 1.35 | fs | Impulse Response (g(t)) Half-Maximum |
| Dielectric Relaxation Time (τε) | ~1 | fs | Human Eye (Day Vision) |
| Dielectric Relaxation Time (τε) | ~1.13 | fs | Diamond |
| Maximum Phase Angle (φmax) | -84 | Degrees | Human Eye (Day Vision) |
| Maximum Phase Angle (φmax) | -86 | Degrees | Human Eye (Night Vision) |
| Maximum Phase Angle (φmax) | -85 | Degrees | Diamond |
| Excitation Wavelength (Diamond) | 532 | nm | Spectrometer-Fluorimeter RAOS-3 |
Key Methodologies
Section titled “Key Methodologies”- Dynamic Link Modeling: The optical environment of the eye and diamond is conceptualized as a dynamic system (link) with an input and output, allowing the application of control theory principles.
- Spectral Curve Approximation: The visibility curves (eye) and luminescence spectra (diamond) are approximated using the Gaussian function G(f) for mathematical tractability.
- Time Domain Analysis: Inertial properties are investigated by feeding the dynamic link with standard signals: the Dirac delta function (δ-function) and the unit function (l(t)).
- Impulse and Transient Response: The system’s reaction to the δ-function yields the impulse characteristic g(t), and the reaction to the unit function yields the transient characteristic h(t).
- Frequency Characteristic Derivation: The complex frequency characteristic w*(f) is obtained by calculating the direct Fourier transform of the impulse characteristic g(t).
- Group Delay Time (GDT) Calculation: The GDT, τ(f), is calculated as the first derivative of the phase spectrum φ(f) with a negative sign, used to assess the time required for electrical neutrality restoration (dielectric relaxation).
- UWB Index Calculation: The UWB index (µ) is calculated using the ratio of the spectrum width (∆f) to the average frequency (fr) to classify the signals as Ultra-Wideband.
Commercial Applications
Section titled “Commercial Applications”- Ophthalmic Implants (IOLs): The demonstrated optical similarity and superior amplification factor (k = 1.41) of diamond compared to other materials support its use in manufacturing high-quality, biocompatible artificial crystalline lenses (IOLs).
- Matrix Photodetector Design: The derived frequency and time characteristics of the human eye serve as an engineering standard (etalon) for creating advanced matrix photodetectors and visual systems that closely mimic human vision.
- Gemological Identification: The unique spectral characteristics and dynamic properties of the diamond can be used as a standard for identifying the origin and authenticity of faceted diamonds (brilliants) of unknown provenance.
- High-Speed Optics and Sensing: The observed Ultra-Wideband (UWB) signal properties and femtosecond-scale dielectric relaxation times suggest potential applications in ultra-fast optical switching and sensing technologies.
View Original Abstract
The paper investigates the frequency characteristics of the spectra of a human eye and a faceted diamond (brilliant). The nrelevance of the research deals with a large number of modern studies on the use of diamond as a lens of the eye. The results obtained were compared with the averaged data (described in the literature) on the visibility curve of day, evening and night vision of the human eye. The research method is based on the representation of the optical environment of the human eye and diamond in the form of a dynamic link with an input and output. The Gaussian function is used to approximate the spectral curves. The study of the inertial properties of such a link in the time domain is performed by feeding signals to its input in the form of a δ-function or a unit function. The steady-state forced oscillations at the output of the investigated dynamic link are found when a harmonic action is applied to the input. Frequency characteristics discover a relationship between the spectra of the input and output signals, representing the direct Fourier transform of the function of time. It was found that the spectra of the visibility of the human eye and the luminescent radiation of diamond have the properties of ultra-wideband signals. It is shown that the amplification of light takes place in the time domain when the width of the spectrum at its half-maximum does not exceed a certain critical value. This phenomenon also manifests itself in the frequency domain. It was revealed that the dynamic links of diamond and human eyes for day and night vision exhibit amplifying properties. Their comparison in terms of the light amplification factor showed their insignificant difference. The results obtained can find application in the creation of matrix photodetectors and as a standard in identifying a faceted diamond (brilliant) of unknown origin and producing a lens from a diamond.